Cube Emitter: the cubes emitted pass through the ground plane instead of rest on it
This answer is just regarding your ground plain and having objects stick to it. I am assuming that this is a particle system. For your ground plane will need to have:


A collision modifier added, then
In the physics field to make them "stick" an option is that you could set Damping to 1 and Friction to 1. However, play around with the fields. 


Note, this image is just using default particles with no mods.



After downloading your blend file I did the same and it worked as expected. Again noting this is only the getting the cube to 'stick' the other part is a bit vague for me.